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Nicole Xiang · 2023年07月21日

请问

  1. CFA I
  2. Quantitative

NO.PZ2015120604000170

问题如下：

A.J. plans to pay his child's tuition fee for four years starting 15 years from now. He estimates the fees is $22,000 per year. If the saving account interest rate is 5.5% annually, and how much payment A.J. should make at the end of each year from now?

选项：

A.

$3,441.23

B.

$3,800.07

C.

$4,009.08

解释：

B is correct.

Step 1: N = 4, FV = 0, I/Y = 5.5, PMT = 22,000, CPT PV = -77,113.30

Step 2: PV =0, N = 14, I/Y = 5.5, FV = 77,113.30, CPT PMT =-$3,800.07

老师，我发现我做类似的题最容易做错的部分就是：前面一个时间段短年份数，就像这道题，我就会按照15年来计算。

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1 个答案

星星_品职助教 · 2023年07月22日

同学你好，

这个问题的本质是先付和后付年金的问题。

先付年金的首笔付款是在年初，也就是说先付年金的现值是和首笔付款在同一个时间点的。例如本题的首笔付款在15时点，那么如果将现值折算到15时点，就相当于认为这是一笔先付年金。但实际题干中并没有说这是先付年金。用先付的方法解决后付的问题，就会出错。

对于后付年金而言，首笔付款是在年末，也就是现值是在首笔付款的前一个时间点上的。首笔付款在15时点，那么现值就应该求到14时点。所以自然就可以得到第二步时的N=14。

简单总结一下，除非题干中给出了先付年金的明确条件，否则都默认按照后付年金来做。如果是后付年金，那么现值就应该求到首笔付款的前一期。这样做，第二步的N就不会算错了。

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